Three men in a cafe order a meal the total cost of which is $15. They each contribute $5.

The waiter takes the money to the chef who recognizes the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14.

Where has the other $1 gone from the original $15?

The payments should equal the receipts. It does not make sense to add what was paid by the men ($12) to what was received from that payment by the waiter ($2)

Although the initial bill was $15 dollars, one of the five dollar notes gets changed into five ones.

The total the three men ultimately paid is $12, as they get three ones back.

So from the $12 the men paid, the owner receives $10 and the waiter receives the $2 difference. $15 – $3 = $10 + $2.